Probabilities of Causation (PoC) play a fundamental role in decision-making in law, health care and public policy. Nevertheless, their point identification is challenging, requiring strong assumptions, in the absence of which only bounds can be derived. Existing work to further tighten these bounds by leveraging extra information either provides numerical bounds, symbolic bounds for fixed dimensionality, or requires access to multiple datasets that contain the same treatment and outcome variables. However, in many clinical, epidemiological and public policy applications, there exist external datasets that examine the effect of different treatments on the same outcome variable, or study the association between covariates and the outcome variable. These external datasets cannot be used in conjunction with the aforementioned bounds, since the former may entail different treatment assignment mechanisms, or even obey different causal structures. Here, we provide symbolic bounds on the PoC for this challenging scenario. We focus on combining either two randomized experiments studying different treatments, or a randomized experiment and an observational study, assuming causal sufficiency. Our symbolic bounds work for arbitrary dimensionality of covariates and treatment, and we discuss the conditions under which these bounds are tighter than existing bounds in literature. Finally, our bounds parameterize the difference in treatment assignment mechanism across datasets, allowing the mechanisms to vary across datasets while still allowing causal information to be transferred from the external dataset to the target dataset.

对于在临床、流行病学和公共政策应用中存在的具有不同治疗方案的外部数据集，提供一种在这种具有挑战性的情景中提供概率因果边界的符号化方法，这些边界适用于任意协变量和治疗的维度，并讨论了这些边界在现有文献中更紧的条件。

合并数据集收紧因果概率界限